[/quote]
,
identical cars on a circular track. Among all of them, they have just enough gas for one car to complete a lap. Show that there is a car that can complete a lap by collecting gas from the other cars on its way around
,
be its circumcenter. Let 
and 
be orthocenters of triangle 
and 
,
be circumcenter of triangle 
.
and circle 
intersect at 
for the second time, prove that 
.
is a polynomial with real coefficients such that![\[ P(x)^2 - 1 = 4 P(x^2 - 4x + 1). \]](http://latex.artofproblemsolving.com/b/4/2/b425a938a1dbbac25e0e0793b30c9e58845d45ab.png)
Find 
and 
be altitudes in an acute triangle 
which meet at 
.
meets the circumcircle of 
and 
such that 
and 
.
and 
meet at 
.
and 
and the line 
concur.
be a diameter of a circle 
,
be the tangent at 
.
be a fixed, positive real, and consider all pairs of points 
and 
lying on 
.
and 
intersect 
and 
,
pass through a common point.
such that
for all 
satisfying 
,
,
,
and 
intersect the altitude from 
to 
respectively. 
is the circumcenter of triangle 
and 
is the reflection of 
is the second intersection of circumcircles of triangles 
and 
.
are collinear.
intersects the altitudes of 
and 
at 
.
lies on a median of triangle 
!
candy bars. Let N & M be positive integers, what is N+M?
.
or 
.
and 
so 
This should be final answer. (Mathdash rating 800)
.
Y by car0t, Exponent11, Chonkachu, PhoenixMathClub, happypi31415
You’ve never seen an AMC 8 quite like this…
We, ChaitraliKA and Aaronjudgeisgoat, present
THE 2026 AMC 8C
Context
This is a totally legit mock test that you can use to predict what your real AMC 8 score will be!
We created many high quality problems for this test, and put our blood, sweat, and tears into it (and if u dont take it we’ll put your blood into it as well). We GUARANTEE that when you take a look at the problems, you will be stunned by the sheer quality oozing out of them. We know this for certain as we got this exact reaction from every single newborn baby that volunteered to take this test. This mock is perfect, not just for people looking to ace the AMC 8 next year, but even for high schoolers.
You have two options on how to take it: Google Docs or MathDash
Google Docs:
Problems
Please read the guidelines carefully, and submit your answers for grading to ChaitraliKA and Aaronjudgeisgoat through AoPS PMs. We will send you the solutions as well, once we have graded you.
MathDash:
https://mathdash.fly.dev/contest/2026amc8c
If you do it on MathDash, we will still send you your final score through AoPS PMs, due to some issues.
We expect to start grading on April 15.
The leaderboard will be updated on the MSM post.
Good luck
!
Please don't get this locked again. I will be very sad if that happens, because this is my 1000th post
. We put a lot of effort into this. If you're going to be a goody-two-shoes, just try to solve the legit problems and ignore the rest.
If you don't want to waste time, here are
We, ChaitraliKA and Aaronjudgeisgoat, present
THE 2026 AMC 8C
Context
This is a totally legit mock test that you can use to predict what your real AMC 8 score will be!
We created many high quality problems for this test, and put our blood, sweat, and tears into it (and if u dont take it we’ll put your blood into it as well). We GUARANTEE that when you take a look at the problems, you will be stunned by the sheer quality oozing out of them. We know this for certain as we got this exact reaction from every single newborn baby that volunteered to take this test. This mock is perfect, not just for people looking to ace the AMC 8 next year, but even for high schoolers.
ChaitraliKA wrote:
This was my first time making a mock, I wanted to make it as realistic as possible. As a person who has never taken an AMC 8 before, I thoroughly researched the types of problems and the format before making this. After some deep analysing, I have come to the conclusion that our mock highly resembles an AMC 8 with a -100% margin of error. I personally enjoyed making this, and put my heart and soul into making the problems and writing out the solutions. There was a lot of collaboration and every question has approval from both of us. As the most respected Cringe Nerdy Mathematician in history, I can guarantee you that it's not only about the math, it's about the experience of taking it. Please scroll down and take the test now. Thank you.
Aaronjudgeisgoat wrote:
After writing a MATHCOUNTS mock, I figured I would try and take it a step further - create an AMC 8 mock. As a fellow person who has never taken an AMC 8 before, I knew there was work needed to be done before I could accurately create one. I thoroughly reviewed the rules for this test, as well as the format. I even made sure to make every single answer choice viable, simulating the silliable nature of the actual AMC 8. We reviewed every single question, answer and solution, and after cross-comparing it with actual MAA exams, I found that it's not 100% accurate to the exam, but 200% accurate. That's right, it's accurate and even more accurate. Overall, this was a very fun experience, creating my first AMC mock so that people in need of math problems have something to work on. I thank @ChaitraliKA for giving me the opportunity to problem write, and I had a very fun time collaborating with the Cringiest and Nerdiest Mathematician of them all. In conclusion, I implore you to click the link below and proceed with the test, as not only will you learn, you will have fun.
Thank you for your blood.
Thank you for your blood.
You have two options on how to take it: Google Docs or MathDash
Google Docs:
Problems
Please read the guidelines carefully, and submit your answers for grading to ChaitraliKA and Aaronjudgeisgoat through AoPS PMs. We will send you the solutions as well, once we have graded you.
MathDash:
https://mathdash.fly.dev/contest/2026amc8c
If you do it on MathDash, we will still send you your final score through AoPS PMs, due to some issues.
We expect to start grading on April 15.
The leaderboard will be updated on the MSM post.
Good luck
!Please don't get this locked again. I will be very sad if that happens, because this is my 1000th post
. We put a lot of effort into this. If you're going to be a goody-two-shoes, just try to solve the legit problems and ignore the rest.If you don't want to waste time, here are
